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# Slack and surplus variables

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. (a) Define the slack and surplus variables. What do they represent? What is (are) the difference(s) between a slack and a surplus variable?

(b) Briefly describe the important parts of each step needed to make a decision using decision sciences models.

(c) What are the different types of special situations that may occur while solving a linear programming problem? Briefly describe each of these special situations.

(d) What are the important properties of a straight line? Briefly describe each property. What are the different types of slopes possible for a straight line? Briefly describe each type of slope and give one example for each type.

2. Given the following linear programming problem

Maximize 20x + 15y
Subject to
2x + 2y < 100
2x + 3y < 120
x > 10
x, y > 0

(a) Graph the constraints.
(b) Find the coordinates of each corner point of the feasible region
(c) Determine the optimal solution.

3. Given that the optimal solution of the following linear programming problem is x = 10 and y = 10, state the problem in standard form and do a constraint analysis for the optimal solution.

Maximize 100x + 80y
Subject to
5x + 2y ≤ 80
3x + 5y ≥ 60
x + y ≤ 20
x ≤ 10
x, y > 0

https://brainmass.com/math/logic/slack-surplus-variables-611589

#### Solution Preview

The response addresses the query posted in 1167 words with APA references

//Linear Programming Problems (LPP) has the great importance in the field of mathematics. It is used for solving the various business problems. The subjects related to the Linear programming problem like slack and surplus variables are used while solving such problems. These are defined and some problems related to it are also solved below. //

a. Slack variables: These variables are put into the constraints for getting the equality constraints and these variables represents the unused peculiarly of resources (Jaiswal, 2012).

Surplus variables: These variables are the representation of the amount by which the value of the solution exceeds a resource. Surplus variables are also known as "Negative Slack Variables".

Slack and surplus variables are used for the purpose of solving Linear Programming Problems (LPP). The variable is added to the constraints when it is in the less than or equal constraints whereas, the surplus variables are applies for the greater or equal constraints (Anderson, et al., 2015).

The important parts of each step needed to make a decision using decision sciences models are:

Problem Statement: the first important part of the decision making is to analyze the problem that is needed to be fixed (Tillman & Cassone, 2012).
Defining objectives: this is the most critical part that has to be defined. The objectives of the study must be clearly defined and known.
Diagnostic Framework: In this part, the decision is made regarding the methods and tools that are to be used in the study.
Collection and Analysis of the data: At this step, the relevant data is collected and further the whole analysis is done.
Make alternative solutions: These are the alternative solutions that are to be taken at this stage excluding the solution conclude from the above steps.
Development of ...

#### Solution Summary

The response addresses the query posted in 1167 words with APA references

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